Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on and models another regular variation on the sub-cone , where is the $i…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
Trend · papers per month
48 results for “regular variations”
Paper develops a new theory on Wasserstein DRO's variation regularization effect.
problem Developing a new theory for Wasserstein DRO's regularization effect.
method General theory on variation regularization effect of Wasserstein DRO.
result New generalization guarantees for adversarial robust learning.
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Study reveals the regularization effect of variational distributions in VAEs.
problem Understanding the regularization role of variational distributions in VAEs.
method Analyzed the role of variational family in VAEs and studied the regularization effect on local geometry.
result Uncovered the implicit regularizer in the -VAE objective and proposed a deterministic autoencoding objective.
The paper tackles variational regularization for manifold-valued data in inverse problems.
problem Inverse problems for manifold-valued data with indirect measurements.
method TV and TGV regularization for manifold-valued data, well-posedness analysis, numerical algorithms.
result Experimental results demonstrate the potential of the proposed schemes.
The paper explores parabolic regularity in geometric variational analysis.
problem Developing calculus rules and computation formulas for second-order generalized differential constructions.
method Introducing and applying the concept of parabolic regularity to geometric aspects of second-order variational analysis.
result Established new calculus rules and computation formulas for second-order generalized differential constructions.
Sparse regular variationstat.ML
New concept of sparse regular variation for better understanding of extreme events.
problem Characterizing the dependence structure of extreme events in multivariate settings.
method Introducing sparse regular variation based on Euclidean projection onto the simplex.
result Sparse regular variation and regular variation are equivalent under mild assumptions.
Multivariate regular variation plays a role assessing tail risk in diverse applications such as finance, telecommunications, insurance and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This pro…
Variational Pseudolikelihood for Regularized Ising Inferencecond-mat.stat-mech
I propose a variational approach to maximum pseudolikelihood inference of the Ising model. The variational algorithm is more computationally efficient, and does a better job predicting out-of-sample correlations than regularized maximum pseudolikelihood inference as well as mean field and isolated spin pair appro…
Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We exhibit examples that illustrate the need for a more general model and discuss de…
Study examines stability of image-reconstruction algorithms using variational regularization.
problem Stability and robustness of image-reconstruction algorithms in medical imaging.
method Review and novel stability results for -regularized linear inverse problems, focusing on .
result Guarantees Lipschitz continuity for small and Hölder continuity for larger in function spaces.
Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Modelcs.LG
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
problem Estimating parameters in Gaussian location model with regularization.
method Ridge-regularized log-density-ratio estimation, variational and spectral approaches.
result Regularized variational estimator has lower risk with many observations, spectral estimator with fewer observations.
This work prevents variational autoencoders from collapsing by adding an auxiliary decoder.
problem Variational autoencoders can collapse into autodecoders, losing semantic information.
method Adding an auxiliary decoder to regularize the latent space.
result Auxiliary decoders increase semantic information in the latent space and reconstructions.
We find the maximum regularization parameter for total-variation denoising.
problem Finding the maximum regularization parameter for anisotropic total-variation denoising.
method Established a closed form expression for the one-dimensional case and an upper-bound for the two-dimensional case using the pseudo-inverse of the divergence.
result The maximum regularization parameter is crucial for optimal parameter tuning and can be computed efficiently.
Optimal regularity for 2D stationary varifolds proved.
problem Regularity of parametrized integer stationary varifolds in 2D.
method Established optimal regularity result for stationary varifolds.
result Smooth minimal branched immersion and constant multiplicity function.
New variational approach to deep learning via gradient descent.
problem Non-robustness and poor out-of-distribution generalization in deep learning.
method Regularize variational neural networks using gradient descent's implicit bias.
result Strong in- and out-of-distribution performance achieved without additional hyperparameter tuning.
The paper studies the smoothness of critical points of variational integrals on Hessian spaces.
problem The study focuses on the regularity of critical points of variational integrals defined on Hessian spaces.
method The approach involves solving a fourth order nonlinear equation and analyzing the Hessian of the critical points.
result Smooth critical points with bounded Hessian are shown to be smooth provided their Hessian has small BMO.
The paper introduces variational characterizations for local entropy and heat regularization in deep learning.
problem Understanding and optimizing loss regularizations in deep learning.
method Introducing variational characterizations and a two-step optimization scheme based on iterative shift and best Gaussian approximation in Kullback-Leibler divergence.
result The optimization schemes for local entropy and heat regularized loss differ only over the argument of the Kullback-Leibler divergence used for best Gaussian approximation.
Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
problem Geometric variational problems, focusing on existence, regularity, and uniqueness of solutions.
method Formulated in Federer and Fleming's theory of currents, discussed the existence theory, and presented core ideas of the (interior) regularity theory for area-minimizing currents and optimal transport paths. Two original results on generic uniqueness of solutions were presented.
result Generic uniqueness of solutions for both Plateau's problem and optimal branched transport problem.
Improves Bayesian neural networks inference efficiency and accuracy.
problem Inflexibility of factorized structure in Dropout posterior.
method Introduces Variational Structured Dropout (VSD) with orthogonal transformation.
result VSD induces adaptive regularization and better generalization.
Proposes a variational approach to shallow neural networks, bypassing optimization.
problem Theoretical understanding and optimization of shallow neural networks.
method Replaces discrete training with a continuum variational surrogate, proving global well-posedness and regularity.
result Optimal parameter density can be obtained by solving a single linear system, achieving generalization error.
Bayesian priors and penalties are equivalent in variational inference.
problem Understanding the relationship between Bayesian priors and penalties in variational inference.
method Characterizing the regularizers that can arise in variational inference and providing a systematic way to compute the prior corresponding to a given penalty.
result Equivalence between Bayesian priors and penalties in variational inference.
Unified variational inference framework reveals GAN's limitations and proposes improvements.
problem Limitations of GAN training and lack of completeness in loss function.
method Reinterpretation of variational inference and revealing special cases of GAN, VAE, etc.
result Proposes a regularization term to improve GAN training stability.
Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computationstat.ML
New method improves approximate inference for Bayesian models.
problem Approximate inference for high-dimensional Bayesian models.
method Entropic regularization of mean-field variational inference.
result Improved recovery of true posterior dependency.
This paper improves VAEs with regularization for better image reconstruction.
problem Improving image reconstruction quality in Variational Autoencoders.
method Least square loss function with regularization for better approximation of data.
result Least square loss function leads to better reconstructed images and faster training.
New insights into tail behavior of heavy-tailed random vectors and processes.
problem Understanding tail behavior of aggregates of heavy-tailed random vectors.
method Analyzing multivariate regularly varying random vectors and Lévy processes.
result More than one large jump can determine tail behavior of aggregates.
Regularizes optimal transport for easier computation and stability.
problem Computational challenges in optimal transport problems.
method Semi-dual formulations and entropic regularization.
result Smooth variational problems for simpler implementation and stability.
Paper proposes Walsh-Hadamard Variational Inference for efficient approximate inference in large models.
problem Over-regularization in variational inference for large models.
method Walsh-Hadamard factorization strategies to reduce parameterization, accelerate computations, and increase posterior expressiveness.
result Efficient approximate inference achieved in over-parameterized models.
Introduces REVE, a regularization scheme that compresses class conditioned entropy.
problem Improving generalization performance of deep learning models.
method Identifies a variable responsible for final prediction, compresses class conditioned entropy, introduces a variational upper bound, and integrates a tractable loss into training.
result Demonstrates the efficiency of REVE on various neural networks and datasets.
Proposes a new method for continual learning in neural networks.
problem Challenges in applying sequential Bayesian inference to neural networks.
method Sequential function-space variational inference.
result Neural networks trained with the proposed method achieve better predictive accuracy.
Study improves oracle inequality for tree graphs using total variation regularization.
problem Improving oracle inequality for tree graphs with total variation regularization.
method Generalized Fused Lasso result to tree graphs, using harmonic mean of distances.
result Proved a lower bound on compatibility constant for total variation penalty.
A PDE approach to the existence and regularity of surfaces of minimum mean curvature variationmath.DG
Analyzes surfaces minimizing mean curvature variation using PDEs.
problem Finding surfaces of minimum mean curvature variation.
method Develops an analytic theory using partial differential equations.
result Establishes existence and regularity of minimizers.
Novel regularization for Vision Transformers improves model generalization and sparsity.
problem Improving generalization and sparsity in Vision Transformers.
method Likelihood-guided variational Ising-based regularization.
result Improved generalization and sparsity in Vision Transformers.
The concept of varifoldmath.DG
Survey of varifolds with focus on their regularity.
problem Understanding the concept and regularity of varifolds.
method Survey and examples of varifolds, emphasizing mean curvature and integral varifolds.
result Emphasis on the regularity of integral varifolds with mean curvature.
On parameters transformations for emulating sparse priors using variational-Laplace inferencestat.ML
Proposes a method to emulate sparse priors using L1 regularization without complex transformations.
problem Sparse priors in under-determined estimation problems.
method Parameter transform to emulate sparse priors under L2 regularization.
result L1 regularization can be achieved with a remapping of parameters under normal priors.
Variational Laplace improves Bayesian neural network performance without sampling.
problem Improving Bayesian neural network performance and calibration.
method Develops a new variational Laplace method for BNNs, exploiting curvature of likelihood.
result Variational Laplace outperforms standard VI methods in test performance and calibration.
Unified regularization framework for visualizing CNNs.
problem Visualizing concepts learned by convolutional neural networks.
method Mathematical framework unifying regularization methods, Sobolev gradients.
result Sobolev filters provide sharper reconstructions and better control over scales.
Extends Campanato theory to multi-valued functions for geometric variational problems.
problem Regularity of multi-valued functions in geometric variational problems.
method Adapting Campanato's ideas to multi-valued functions, proving regularity theorems.
result Established regularity for multi-valued harmonic functions and stationary integral varifolds.
What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theorystat.ML
New framework explains deep neural networks using variational spline theory.
problem Understanding functions learned by deep neural networks.
method Developed a variational framework and function space.
result Deep ReLU networks are solutions to regularized data fitting problems over the proposed function space.
GAN+VER improves GANs by regularizing entropy to reduce mode collapse.
problem Mode collapse in GANs where the generator fails to capture all modes.
method Maximizing a variational lower bound on the entropy of generated samples.
result Significant improvement in evaluation metrics for real and generated samples.
Study compares L1 and VG sparsity priors in inverse problems.
problem Sparse regularization in inverse problems with incomplete or corrupted measurements.
method Compared L1 regularization with Variational Garrote (VG), a probabilistic method approximating L0 sparsity.
result VG often achieves lower minimum generalization error and improved stability in strongly underdetermined regimes.
Batch norm with entropic regularization turns deterministic autoencoders into generative modelscs.LG
Batch normalization with regularization turns deterministic autoencoders into generative models.
problem Creating generative models from deterministic autoencoders.
method Using batch normalization as a source of non-determinism and adding entropic regularization.
result Deterministic autoencoders can be transformed into generative models with similar performance to variational autoencoders.
New method prevents neural network breakdown by combining trimmed loss and variation regularization.
problem Outlier contamination in neural network training.
method Integrates transformed trimmed loss and higher-order variation regularization.
result Ensures robustness to outlier contamination with a high functional breakdown point.
A new method reduces over-regularization in Bayesian deep learning.
problem Bayesian inference for over-parameterized models is challenging.
method Walsh-Hadamard Variational Inference (WHVI) using factorization strategies.
result WHVI avoids over-regularization issues and yields speedups and model reductions.
New variational methods find close-to-conformal and isometric immersions of surfaces.
problem Finding conformal and isometric immersions of surfaces.
method Variational functionals for spinor fields on compact Riemann surfaces.
result Minimization of variational functionals can yield piecewise smooth isometric immersions.
Proposes regularization for robust image models using Wasserstein geometry.
problem Robustness to in-class variations in input data.
method Wasserstein-2 geometry, Tikhonov-type regularizer, data augmentation.
result Improves generalization under adversarial perturbations and large variations.
The paper develops a multi-kernel method with sparsity constraint for regression.
problem Developing a robust regression method with sparsity constraints.
method Banach-space formulation, generalized total-variation regularization, multi-kernel expansion, adaptive kernel positions, penalty on coefficients.
result The method achieves sparsity in the kernel coefficients, reducing the number of active kernels to the number of data points.
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given -smooth data, we prove -regularity of solutions up t…